Communications in Mathematical Physics

, Volume 123, Issue 4, pp 641–658 | Cite as

Morse theory interpretation of topological quantum field theories

  • J. M. F. Labastida


Topological quantum field theories are interpreted as a generalized form of Morse theory. This interpretation is applied to formulate the simplest topological quantum field theory: topological quantum mechanics. The only non-trivial topological invariant corresponding to this theory is computed and identified with the Euler characteristic. Using field theoretical methods this topological invariant is calculated in different ways and in the process a proof of the Gauss-Bonnet-Chern-Avez formula as well as some results of degenerate Morse theory are obtained.


Neural Network Statistical Physic Field Theory Complex System Quantum Field Theory 
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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • J. M. F. Labastida
    • 1
  1. 1.Theory DivisionCERNGeneva 23Switzerland

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